Metamath Proof Explorer

Theorem simplbi2VD

Description: Virtual deduction proof of simplbi2 . The following user's proof is completed by invoking mmj2's unify command and using mmj2's StepSelector to pick all remaining steps of the Metamath proof.

h1::	\|- ( ph <-> ( ps /\ ch ) )
3:1,?: e0a	\|- ( ( ps /\ ch ) -> ph )
qed:3,?: e0a	\|- ( ps -> ( ch -> ph ) )

The proof of simplbi2 was automatically derived from it. (Contributed by Alan Sare, 31-Dec-2011) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Hypothesis	pm3.26bi2VD.1	⊢ ( 𝜑 ↔ ( 𝜓 ∧ 𝜒 ) )
	Assertion	simplbi2VD	⊢ ( 𝜓 → ( 𝜒 → 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		pm3.26bi2VD.1	⊢ ( 𝜑 ↔ ( 𝜓 ∧ 𝜒 ) )
2		biimpr	⊢ ( ( 𝜑 ↔ ( 𝜓 ∧ 𝜒 ) ) → ( ( 𝜓 ∧ 𝜒 ) → 𝜑 ) )
3	1 2	e0a	⊢ ( ( 𝜓 ∧ 𝜒 ) → 𝜑 )
4		pm3.3	⊢ ( ( ( 𝜓 ∧ 𝜒 ) → 𝜑 ) → ( 𝜓 → ( 𝜒 → 𝜑 ) ) )
5	3 4	e0a	⊢ ( 𝜓 → ( 𝜒 → 𝜑 ) )